Let n be a positive integer. We defineWe then form the sequence obtained  by iterating  T:...

Let n be a positive integer. We define

We then form the sequence obtained  by iterating  T: n.  T(n),  T(T(n),  T(T(T(n))). … For instance, starting with n = 7, we have 7, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, …. A well-known conjecture, sometimes called the Collar conjecture, asserts that the sequence obtained by iterating T always reaches the integer 1 no matter which positive integer n begins the sequence.

Show that the Collatz conjecture is true if it can be shown that for every positive integer n with n ≥ 2 there is a term in tie sequence obtained by iterating T that is less than n.